Knight's open tour on 5X5 board

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I'm trying to write a program that finds an open knight's tour on 5X5 board starting from every point. I So the question is does every point actually has a solution. I found this answer that says that there is no solution when you start at any of the squares adjacent to a corner square. However when I run a program I get solutions only when I start in the points marked with k

 k| |k| |k
  |k| |k| 
 k| |k| |k
  |k| |k| 
 k| |k| |k